Vassili Kitsios

BiGlobal stability analysis in curvilinear coordinates of massively separated lifting bodies

A methodology based on spectral collocation numerical methods for global flow stability analysis of incompressible external flows is presented. A potential shortcoming of spectral methods, namely the handling of the complex geometries encountered in global stability analysis, has been dealt with successfully in past works by the development of spectral-element methods on unstructured meshes. The present contribution shows that a certain degree of regularity of the geometry may be exploited in order to build a global stability analysis approach based on a regular spectral rectangular grid in curvilinear coordinates and conformal mappings. The derivation of the stability linear operator in curvilinear coordinates is presented along with the discretisation method. Unlike common practice to the solution of the same problem, the matrix discretising the eigenvalue problem is formed and stored. Subspace iteration and massive parallelisation are used in order to recover a wide window of its leading Ritz system. The method is applied to two external flows, both of which are lifting bodies with separation occurring just downstream of the leading edge. Specifically the flow configurations are a NACA 0015 airfoil, and an ellipse of aspect ratio 8 chosen to closely approximate the geometry of the airfoil. Both flow configurations are at an angle of attack of 18^o with a Reynolds number based on the chord length of 200. The results of the stability analysis for both geometries are presented and illustrate analogous features.

Subgrid Model with Scaling Laws for Atmospheric Simulations

AbstractSubgrid-scale parameterizations with self-similar scaling laws are developed for large-eddy simulations (LESs) of atmospheric flows. The key new contribution is the development of scaling laws that govern how these parameterizations depend on the LES resolution and flow strength. Both stochastic and deterministic representations of the effects of subgrid-scale eddies on the retained scales are considered. The stochastic subgrid model consists of a backscatter noise term and a drain eddy viscosity, while in the deterministic subgrid model the net effect of these two terms is represented by a net eddy viscosity. In both cases the subgrid transfers are calculated self-consistently from the statistics of higher-resolution-reference direct numerical simulations (DNSs). The dependence of the subgrid parameterizations on the resolution of the LESs is determined for DNSs having resolutions up to triangular 504 wavenumber truncations. The subgrid parameterizations are developed for typical large-scale atmo...

Proposed stochastic parameterisations of subgrid turbulence in large eddy simulations of turbulent channel flow

Stochastic and deterministic subgrid parameterisations are developed for the large eddy simulation (LES) of a turbulent channel flow with friction-velocity-based Reynolds number of Reτ = 950 and centreline-based Reynolds number of Re0 = 20,580. The subgrid model coefficients (eddy viscosities) are determined from the statistics of truncated reference direct numerical simulations (DNSs). The stochastic subgrid model consists of a mean-field shift, a drain eddy viscosity acting on the resolved field and a stochastic backscatter force of variance proportional to the backscatter eddy viscosity. The deterministic variant consists of a net eddy viscosity acting on the resolved field, which represents the net effect of the drain and backscatter. LES adopting the stochastic and deterministic models is shown to reproduce the time-averaged kinetic energy spectra of the DNS within the resolved scales.

Scaling laws for parametrizations of subgrid interactions in simulations of oceanic circulations

Parametrizations of the subgrid eddy–eddy and eddy–meanfield interactions are developed for the simulation of baroclinic ocean circulations representative of an idealized Antarctic Circumpolar Current. Benchmark simulations are generated using a spectral spherical harmonic quasi-geostrophic model with maximum truncation wavenumber of T=504, which is equivalent to a resolution of 0.24° globally. A stochastic parametrization is used for the eddy–eddy interactions, and a linear deterministic parametrization for the eddy–meanfield interactions. The parametrization coefficients are determined from the statistics of benchmark simulations truncated back to the large eddy simulation (LES) truncation wavenumber, TR<T. A stochastic technique is used to determine the eddy–eddy coefficients, and a new least-squares regression method for the eddy–meanfield terms. Truncations are repeated for various TR, and the resolution dependence of the subgrid coefficients is identified. The mean jet structure and the kinetic and potential energy spectra resulting from the LESs closely agree with those from the benchmark simulations.

BiGlobal Instability Analysis of Turbulent Flow Over an Airfoil at an Angle of Attack

Stability analysis can provide insight to aerodynamic flow control studies by numerical means. It is advantageous to use spectral numerical methods for the stability analysis as they are, at the same level of numerical effort, more accurate than standard finite volume or finite element alternatives. The disadvantage with classic spectral collocation methods, however, is the difficulty in handling geometry. While spectrally accurate and geometrically flexible methods (TSB) exist, based on the spectral/hp−element concept, this paper will present a means of undertaking a fluid mechanical instability analysis using spectral collocation numerical methods on a rectangular grid and conformal mapping techniques in order to represent the geometry of the problem. The flow control configuration of interest in this study is the leading edge separation of a NACA 0015 airfoil, at an angle of attack α = 18. Water tunnel experiments of this configuration, were undertaken by for a Rec ≡ U∞c/ν = 3× 10, where c is the length of the airfoil chord, U∞ is the freestream velocity, and ν the kinematic viscosity. The flow was perturbed via a zero-net-mass-flux (ZNMF) jet, normal to the surface, and spanned the entire leading edge. Frequencies F ≡ fc/U∞ = 0.65 and from F = 1.1 → 1.4 were found to enhanced the lift by more than 45%. A Large Eddy Simulation (LES) of the uncontrolled case was undertaken, and the largest frequency component of the lift force history was F = 0.63, corresponding to one of the frequencies that were found to significantly enhance the lift in the experimental study. The work presented within will introduce the development work of the conformal mapping and numerical techniques required to enable the spectral analysis of this flow configuration. In order to separate the conformal mapping development procedure from that of unsteadiness in the flow, here a lower Rec = 200 is first adopted at which the flow is laminar and steady, then the analysis is repeated at a slightly higher Rec = 300 at which the flow is laminar and unsteady. Results at the target Reynolds number of the turbulent flow at Rec = 3× 10 will be presented elsewhere. The paper will be organised as follows. Firstly an overview of the experimental study will be presented, followed by a comparison of experimental results with those obtained by applying the finite-volume Stanford CDP LES solver to this problem. In addition, a second order finite-element solver (ADFC) has been used to obtain basic states. Next, the derivation of the stability linear operator will be outlined, including a discussion of numerical aspects on the general curvilinear coordinate system, in particular the means of transforming the geometry and velocities between coordinate systems. Following this, two specific geometries are chosen in order to highlight the proposed analysis methodology. An 8:1 ellipse placed at an angle of attack α = 18 to the oncoming flow is first analysed, as the analytical derivatives required for the conformal mapping

Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation

The statistical properties are presented for the direct numerical simulation (DNS) of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation. The APG TBL has a momentum thickness based Reynolds number range from

Stochastic self-energy subgrid model for the large eddy simulation of turbulent channel flows

Re_{\delta_2}=570

Stochastic Subgrid Modelling for Geophysical and Three-Dimensional Turbulence

to

Recovery of the Koopman Modes of a Leading-Edge Separated Aerofoil Flow via a Proper Orthogonal Decomposition Rank Reduction

13800

Towards the Direct Numerical Simulation of a Self-similar Adverse Pressure Gradient Turbulent Boundary Layer Flow

, with a self-similar region from